Note that the mean and standard deviation of the Poisson random variable are both lambda. So, look back at Chebyshev and see where these values fit in.

P(|x-mu|<k*(sigma)) >= 1-(1/k^2)

If we subtract this probability from 1 we should get P([-k*(sigma) >= x-mu]or[x-mu >= k*(sigma)]) ...

Excuse my excessive use of brackets.